Editing Hypothetical syllogism (section)

==Propositional logic==
In [[propositional logic]], '''hypothetical syllogism''' is the name of a valid [[rule of inference]] (often abbreviated '''HS''' and sometimes also called the '''chain argument''', '''chain rule''', or the principle of '''transitivity of implication'''). The rule may be stated:

:<math>\frac{P \to Q, Q \to R}{\therefore P \to R}</math>

In other words, whenever instances of "<math>P \to Q</math>", and "<math>Q \to R</math>" appear on lines of a [[formal proof|proof]], "<math>P \to R</math>" can be placed on a subsequent line.